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Nonlinear snap-buckling and resonance of FG-GPLRC curved beams with different boundary conditions

  • Lei-Lei Gan (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University)
  • 투고 : 2022.12.16
  • 심사 : 2023.02.15
  • 발행 : 2023.03.10

초록

Snap-buckling is one of the main failure modes of structures, because it will lead to the reduction of structural bearing capacity, durability loss and even structural damage. Boundary condition plays an important role in the research of engineering mechanics. Further discussion on the boundary conditions problems will help to analyze the dynamic and static behavior of structures more accurately. Therefore, in order to understand the dynamic and static behavior of curved beams more comprehensively, this paper mainly studies the nonlinear snap-through buckling and forced vibration characteristics of functionally graded graphene reinforced composites (FG-GPLRCs) curved beams with two different boundary conditions (including clamped-hinged and hinged-hinged) using Euler-Bernoulli beam theory (E-BBT). In addition, the effects of the curved beam radius, the GLPs distributions, number of GLPs layers, the mass fraction of GLPs and elastic foundation parameters on the nonlinear snap-through buckling and forced vibration behavior are discussed respectively.

키워드

참고문헌

  1. Abumandour, R.M., El-Shorbagy, M.A., Eldesoky, I.M., Kamel, M.H., Alotaibi, H. and Felila, A.L. (2022), "Deflection analysis of a nonlocal euler-bernoulli nanobeam model resting on two elastic foundations: A generalized differential quadrature approach", Symmetry-basel, 14(11), 2342. https://doi.org/10.3390/sym14112342.
  2. Al-Furjan, M.S.H., Yin, C., Shen, X., Kolahchi, R., Zarei, M.S. and Hajmohammad, M.H. (2022), "Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate", Mech. Syst. Signal. Pr., 178, 109269. https://doi.org/10.1016/j.ymssp.2022.109269.
  3. Alazwari, M.A., Daikh, A.A., Houari, M.S., Tounsi, A. and Eltaher, M.A. (2021), "On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations", Steel. Compos. Struct., 40(3), 389-404. https://doi.org/10.12989/scs.2021.40.3.389.
  4. Amir, M., Kim, S.W. and Talha, M. (2022), "On the stochastic vibration analysis of the geometrically nonlinear graded cellular curved panels with material stochasticity", Int. J. Pres. Ves. Pip., 199, 104768. https://doi.org/10.1016/j.ijpvp.2022.104768.
  5. Assie, A.E., Mohamed, S.A., Shanab, R.A., Abo-bakr, R.M. and Eltaher, M.A. (2023), "Static buckling of 2D FG porous plates resting on elastic foundation based on unified shear theories", J. Appl. Comput. Mech., 9(1), 239-258. https://doi.org/10.22055/jacm.2022.41265.3723.
  6. Babaei, H. (2021), "On frequency response of FG-CNT reinforced composite pipes in thermally pre/post buckled configurations", Compos. Struct., 276, 114467. https://doi.org/10.1016/j.compstruct.2021.114467.
  7. Babaei, H. (2022a), "Nonlinear analysis of size‑dependent frequencies in porous FG curved nanotubes based on nonlocal strain gradient theory", Eng. Struct., 38, 1717-1734. https://doi.org/10.1007/s00366-021-01317-7.
  8. Babaei, H. (2022b), "Free vibration and snap-through instability of FG-CNTRC shallow arches supported on nonlinear elastic foundation", Appl. Math. Comput., 413, 126606. https://doi.org/10.1016/j.amc.2021.126606.
  9. Babaei, H. and Eslami, M.R. (2021a), "Nonlinear analysis of thermalmechanical coupling bending of FGP infinite length cylindrical panels based on PNS and NSGT", Appl. Math. Model., 91, 1061-1080. https://doi.org/10.1016/j.apm.2020.10.004
  10. Babaei, H. and Eslami, M.R. (2021b), "Nonlinear analysis of thermalmechanical coupling bending of clamped FG porous curved microtubes", J. Therm. Stresses, 44(4), 409-432. https://doi.org/10.1080/01495739.2020.1870417.
  11. Babaei, H., Kiani, Y. and Eslami, M.R. (2018a), "Geometrically nonlinear analysis of functionally graded shallow curved tubes in thermal environment", Thin-Walled Struct., 132, 48-57. https://doi.org/10.1016/j.tws.2018.08.008.
  12. Babaei, H., Kiani, Y. and Eslami, M.R. (2018b), "Geometrically nonlinear analysis of shear deformable FGM shallow pinned arches on nonlinear elastic foundation under mechanical and thermal loads", Acta. Mech., 229(7), 3123-3141. https://doi.org/10.1007/s00707-018-2134-2.
  13. Babaei, H., Kiani, Y. and Eslami, M.R. (2018c), "Application of two-steps perturbation technique to geometrically nonlinear analysis of long FGM cylindrical panels on elastic foundation under thermal load", J. Therm, Stress., 41(7), 847-865. https://doi.org/10.1080/01495739.2017.1421054.
  14. Babaei, H., Kiani, Y. and Eslami, M.R. (2019a), "Thermal buckling and post-buckling analysis of geometrically imperfect FGM clamped tubes on nonlinear elastic foundation", Appl. Math. Model., 71, 12-30. https://doi.org/10.1016/j.apm.2019.02.009.
  15. Babaei, H., Kiani, Y. and Eslami, M.R. (2019b), "Large amplitude free vibration analysis of shear deformable FGM shallow arches on nonlinear elastic foundation", Thin-Walled Struct., 144, 48-57. https://doi.org/10.1016/j.tws.2019.106237.
  16. Babaei, H., Kiani, Y. and Eslami, M.R. (2019c), "Large amplitude free vibrations of long FGM cylindrical panels on nonlinear elastic foundation based on physical neutral surface", Compos. Struct., 220, 888-898. https://doi.org/10.1016/j.compstruct.2019.03.064.
  17. Babaei, H., Kiani, Y. and Eslami, M.R. (2019d), "Buckling and post-buckling analysis of geometrically imperfect FGM pin-ended tubes surrounded by nonlinear elastic medium under compressive and thermal loads", Int. J. Mech. Mater. Des., 15(2), 225-244. https://doi.org/10.1007/s10999-018-9420-y.
  18. Babaei, H., Kiani, Y. and Eslami, M.R. (2019e), "Thermomechanical nonlinear in-plane analysis of fix-ended FGM shallow arches on nonlinear elastic foundation using two-step perturbation technique", Int. J Struct. Stab. Dynam., 19(8), 1950089. https://doi.org/10.1142/S0219455419500895.
  19. Basha, M., Daikh, A.A., Melaibari, A., Wagih, A., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahman, A. and Eltaher, M.A. (2022), "Nonlocal strain gradient theory for buckling and bending of FG-GRNC laminated sandwich plates", Steel. Compos. Struct., 43(5), 639-660. https://doi.org/10.12989/scs.2022.43.5.639.
  20. Chaabani, H., Mesmoudi, S., Boutahar, L. and El Bikri, K. (2022), "Buckling of porous FG sandwich plates subjected to various nonuniform compressions and resting on Winkler-Pasternak elastic foundation using a finite element model based on the high-order shear deformation theory", Acta. Mech., 233(12), 5359-5376. https://doi.org/10.1007/s00707-022-03388-z.
  21. Chen, J.S., Wen, Q.W. and Yeh, C. (2022), "Steady state responses of an infinite beam resting on a tensionless visco-elastic foundation under a harmonic moving load", J. Sound. Vib., 540, 17298. https://doi.org/10.1016/j.jsv.2022.117298.
  22. Chen, R., Wang, W., Wu, K., Zheng, G., Xu, X.J., Wang, H.G. and Luo, J. (2023), "Design and optimization of a novel compliant planar parallelogram mechanism utilizing initially curved beams", Mech. Mach. Theory., 179, 105092. https://doi.org/10.1016/j.mechmachtheory.2022.105092.
  23. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Luo, J. and Pu, H.Y. (2022a), "On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment", Eur. Phys. J. Plus., 137(10), 1158. https://doi.org/10.1140/epjp/s13360-022-03234-0.
  24. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Pu, H.Y. and Luo, J. (2022b), "Nonlinear free vibration analysis of functionally graded carbon nanotube reinforced fluid-conveying pipe in thermal environment", Steel. Compos. Struct., 45(5), 641-652. https://doi.org/10.12989/scs.2022.45.5.641.
  25. Chinnapandi, L.B.M., Pitchaimani, J. and Eltaher, M.A. (2022), "Vibro-acoustics of functionally graded porous beams subjected to thermo-mechanical loads", Steel. Compos. Struct., 44(6), 815-829. https://doi.org/10.12989/scs.2022.44.6.815.
  26. Daikh, A.A., Belarbi, M.O., Ahmed, D., Houari, M.S.A., Avcar, M., Tounsi, A., and Eltaher, M.A. (2022), "Static analysis of functionally graded plate structures resting on variable elastic foundation under various boundary conditions", Acta. Mech., https://doi.org/10.1007/s00707-022-03405-1.
  27. Deng, L.F., Niu, M.Q., Xue, J. and Chen, L.Q. (2023), "An ALE formulation for the geometric nonlinear dynamic analysis of planar curved beams subjected to moving loads", Mech. Syst. Signal. Pr., 184, 109670. https://doi.org/10.1016/j.ymssp.2022.109670.
  28. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. https://doi.org/10.12989/sem.2021.80.1.063.
  29. Ding, H.X., She, G.L. and Zhang, Y.W. (2022a), "Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection", Eur. Phys. J. Plus, 137,1329. https://doi.org/10.1140/epjp/s13360-022-03570-1.
  30. Ding, H.X., Zhang, Y.W. and She, G.L. (2022b), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concrete, 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433.
  31. Eltaher, M.A., Mohamed, N., Mohamed, S.A. and Seddek, L.F. (2019), "Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations", Appl. Math. Model., 75, 414-445. https://doi.org/10.1016/j.apm.2019.05.026.
  32. Ermis, M., Kutlu, A., Eratli, N. and Omurtag, M.H. (2022), "Free vibration of axially FG curved beam on orthotropic Pasternak foundation via mixed FEM", J. Braz. Soc. Mech. Sci., 44(12), 597. https://doi.org/10.1007/s40430-022-03853-9.
  33. Esmaeili, H.R., and Kiani, Y. (2022), "Vibrations of graphene platelet reinforced composite doubly curved shells subjected to thermal shock", Mech. Based. Des. Struct., https://doi.org/10.1080/15397734.2022.2120499.
  34. Gao, Y., Xiao, W.S. and Zhu, H.P. (2020), "Snap-buckling of functionally graded multilayer graphene platelet-reinforced composite curved nanobeams with geometrical imperfections", Eur. J. Mech. A-Solid., 82, 103993. https://doi.org/10.1016/j.euromechsol.2020.103993.
  35. Hendi, A., Eltaher, M.A, Mohamed, S.A. and Attia, M. (2022), "Nonlinear thermal vibration of pre/post-buckled two-dimensional FGM tapered microbeams based on a higher order shear deformation theory", Steel Compos. Struct., 41(6), 787-802. http://doi.org/DOI10.12989/scs.2021.41.6.787.
  36. Homaeinezhad, M.R. and Gavari, M.A. (2022), "Feedback control of actuation-constrained moving structure carrying Timoshenko beam", Int. J. Robust. Nonlin., https://doi.org/10.1002/rnc.6471.
  37. Hu, S.W., Zhong, R., Wang, Q.S., Qin, B., and Shao, W. (2022), "A strong-form Chebyshev-RPIM meshless solution for free vibration of conical shell panels with variable thickness and fiber curvature", Compos. Struct., 296, 115884. https://doi.org/10.1016/j.compstruct.2022.115884.
  38. Huang, W.C., Qin, L.H. and Chen, Q. (2022), "Numerical exploration on snap buckling of a pre-stressed hemispherical gridshell", J. Appl. Mech -T. ASME., 89(1), 011005. https://doi.org/10.1115/1.4052289.
  39. Jiang, Y.L., Sun, H.Y. and Yan, H.J. (2022), "Vibration-impact study on the functionally graded graphene nanoplatelets reinforced composite curved open-type shell", Wave. Random. Complex, https://doi.org/10.1080/17455030.2022.2117875
  40. Kallannavar, V. and Kattimani, S. (2023), "Effect of temperature and porosity on free vibration characteristics of a doubly-curved skew laminated sandwich composite structures with 3D printed PLA core", Thin. Wall. Struct., 182, 110263. https://doi.org/10.1016/j.tws.2022.110263.
  41. Li, C., Shen, H.S. and Yang, J. (2022), "Design and nonlinear dynamics of FG curved sandwich beams with self-adapted auxetic 3D double-V meta-lattice core", Eng. Struct., 272, 115023. https://doi.org/10.1016/j.engstruct.2022.115023.
  42. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.
  43. Malikan, M., Tornabene, F. and Dimitri, R. (2019), "Transient response of oscillated carbon nanotubes with an internal and external damping", Compos. Part B: Eng., 158, 198-205. https://doi.org/10.1016/j.compositesb.2018.09.092.
  44. Malikan, M., Wiczenbach, T. and Eremeyev, V.A. (2022), "Thermal buckling of functionally graded piezomagnetic micro-and nanobeams presenting the flexomagnetic effect", Continuum Mech. Thermodynam., 34(4), 1051-1066. https://doi.org/10.1007/s00161-021-01038-8.
  45. Melaibari, A., Mohamed, S.A., Assie, A.E., Shanab, R.A. and Eltaher, M.A. (2023), "Static response of 2D FG porous plates resting on elastic foundation using midplane and neutral surfaces with movable constraints", Mathematics, 10(24), 4784. https://doi.org/10.3390/math10244784.
  46. Melchiorre, J., Manuello, A., Marmo, F., Adriaenssens, S. and Marano, G.C. (2023), "Differential formulation and numerical solution for elastic arches with variable curvature and tapered crosssections", Eur. J. Mech. A-Solid, 97, 104757. https://doi.org/10.1016/j.euromechsol.2022.104757.
  47. Mohamed, N., Mohamed, S.A. and Eltaher, M.A. (2021), "Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model", Eng. with Comput., 37(4), 2823-2836. http://dx.doi.org/10.1007/s00366-020-00976-2.
  48. Mohamed, S.A., Mohamed, N. and Eltaher, M.A. (2022), "Snap-through instability of helicoidal composite imperfect beams surrounded by nonlinear elastic foundation", Ocean. Eng., 263, 112171. https://doi.org/10.1016/j.oceaneng.2022.112171.
  49. Pham, H.A., Tran, H.Q., Tran, M.T., Nguyen, V. and Huong, Q.T. (2022), "Free vibration analysis and optimization of doubly-curved stiffened sandwich shells with functionally graded skins and auxetic honeycomb core layer", Thin. Wall. Struct., 179, 109571. https://doi.org/10.1016/j.tws.2022.109571.
  50. Pham, Q.H., Tran, V.K. and Nguyen, P.C. (2022), "Hygro-thermal vibration of bidirectional functionally graded porous curved beams on variable elastic foundation using generalized finite element method", Case. Stud. Therm. Eng., 40, 102478. https://doi.org/10.1016/j.csite.2022.102478.
  51. Pham, Q.H., Tran, V.K., Tran, T.T., Nguyen, P.C. and Malekzadeh, P. (2022), "Dynamic instability of magnetically embedded functionally graded porous nanobeams using the strain gradient theory", Alex. Eng. J., 61(12), 10025-10044. https://doi.org/10.1016/j.aej.2022.03.007.
  52. Qiao, W.Z., Guo, T.D., Kang, H.J. and Zhao, Y.Y. (2022), "An asymptotic study of nonlinear coupled vibration of arch-foundation structural system", Eur. J. Mech. A-Solid., 96, 104711. https://doi.org/10.1016/j.euromechsol.2022.104711.
  53. Shahmohammadi, M.A., Mirfatah, S.M., Salehipour, H. and Civalek, O. (2023), "On nonlinear forced vibration of micro scaled panels", Int. J. Eng. Sci., 182, 103774. https://doi.org/10.1016/j.ijengsci.2022.103774.
  54. She, G.L. (2020), "Wave propagation of FG polymer composite nanoplates reinforced with GNPs", Steel Compos. Struct., 37(1) , 27-35. https://doi.org/10.12989/scs.2020.37.1.027.
  55. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stresses, 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  56. She, G.L. and Ding, H.X. (2023), "Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Acta Mech. Sin., 39, 522392. https://doi.org/10.1007/s10409-022-22392-x.
  57. She, G.L. and Li, Y.P. (2022), "Wave propagation in an FG circular plate in thermal environment", Geomech. Eng., 31(6), 615-622. https://doi.org/10.12989/gae.2022.31.6.615.
  58. She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232. https://doi.org/10.12989/sem.2022.82.2.225.
  59. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407
  60. Tornabene, F., Viscoti, M. and Dimitri, R. (2022), "Higher order theories for the free vibration analysis of laminated anisotropic doubly-curved shells of arbitrary geometry with general boundary conditions", Compos. Struct., 297, 115740. https://doi.org/10.1016/j.compstruct.2022.115740.
  61. Tornabene, F., Viscoti, M. and Dimitri, R. (2023), "Static analysis of anisotropic doubly-curved shell subjected to concentrated loads employing higher order layer-wise theories", Cmes -Comp. Model. Eng., 134(2), 1393-1468. https://doi.org/10.32604/cmes.2022.022237.
  62. Tung, H.V. (2018), "Nonlinear thermomechanical response of pressure-loaded doubly curved functionally graded material sandwich panels in thermal environments including tangential edge constraints", J. Sandw. Struct. Mater., 20(8), 974-1008. https://doi.org/10.1177/1099636216684312.
  63. Van Long, N., Thinh, T.I., Bich, D.H. and Tu, T.M. (2022), "Nonlinear dynamic responses of sandwich-FGM doubly curved shallow shells subjected to underwater explosions using first-order shear deformation theory", Ocean. Eng., 260, 111886. https://doi.org/10.1016/j.oceaneng.2022.111886.
  64. Wang, X.S., Wu, S.B., Yin, J.M., Moradi, Z., Safa, M. and Khadimallah, M.A. (2023), "On the electromechanical energy absorption of the reinforced composites piezoelectric MEMS via Adaptive neuro-fuzzy inference system and MCS theory", Compos. Struct., 303, 116246. https://doi.org/10.1016/j.compstruct.2022.116246.
  65. Xiong, Z.H., Kou, L., Zhao, J.J., Cui, H. and Wang, B. (2022), "Isogeometric analysis of longitudinal displacement of a simplified tunnel model based on elastic foundation beam", Cmes-Comp. Model. Eng. https://doi.org/10.32604/cmes.2023.024833.
  66. Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329.
  67. Zhai, Y.J., Ma, Z.S., Ding, Q. and Wang, X.P. (2023), "Nonlinear transverse vibrations of a jointed structure with two slightly curved beams connected by complex elastic joints", Int. J. Nonlin. Mech., 148, 104259. https://doi.org/10.1016/j.ijnonlinmec.2022.104259.
  68. Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel. Compos, Struct., 42(3) 397-405. https://doi.org/10.12989/scs.2022.42.3.397.
  69. Zhang, Y.W. and She, G.L. (2023a), "Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection", Nonlinear Dynam., https://doi.org/10.1007/s11071-022-08186-9.
  70. Zhang, Y.W. and She, G.L. (2023b), "Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment", Mech. Adv. Mater. Struct., https://doi.org/10.1080/15376494.2023.2180556.
  71. Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stresses, 45(12), 1029-1042. https://doi.org/10.1080/01495739.2022.2125137.
  72. Zhang, Y.W., Ding, H.X. and She, G.L. (2023a), "Wave propagation in spherical and cylindrical panels reinforced with carbon nanotubes", Steel Compos. Struct., 46(1), 133-141. https://doi.org/10.12989/scs.2023.46.1.133.
  73. Zhang, Y.W., She, G.L. and Ding, H.X. (2023b), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A-Solid., 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887.
  74. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTRC curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.
  75. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022a), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel. Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.
  76. Zhao, J.L., She, G.L., Wu, F., Yuan, S.J., Bai, R.Q., Pu, H.Y., Wang, S.L. and Luo, J. (2022b), "Guided waves of porous FG nanoplates with four edges clamped", Adv. Nano. Res., 13(5), 465-474. https://10.12989/anr.2022.13.5.465.